Two circular coils of radius R, each carrying a current I in the same sense, are parallel with the xy-plane with their centers at (0, 0, ±d/2). On the z-axis the magnetic field is B' = B (z)z^. At z = 0, halfway between the coils, B/az = 0.
(i) Determine d such that ∂2B/∂z2 = 0 at z = 0 on the z-axis.
(ii) Show that for this configuration, the third derivative of the field with respect to z is also zero at z = 0.
(iii) Use a computer to plot the magnetic field B(z) as a function of position z along the axis.